GIÁO TRÌNH MARKETING NGHIÊN CỨU - PHẦN 18 pptx

Determining and
Interpreting Associations
Among Variables
Ch 18 2
Associative Analyses
•
Associative analyses: determine
where stable relationships exist
between two variables
•
Examples
–
What methods of doing business are
associated with level of customer satisfaction?
–
What demographic variables are associated
with repeat buying of Brand A?
–
Is type of sales training associated with sales
performance of sales representatives?
–
Are purchase intention scores of a new product
associated with actual sales of the product?
Ch 18 3
Relationships Between Two
Variables
•
Relationship: a consistent, systematic
linkage between the levels or labels for
two variables

•
“Levels” refers to the characteristics of
description for interval or ratio scales…the
level of temperature, etc.
•
“Labels” refers to the characteristics of
description for nominal or ordinal scales,
buyers v. non-buyers, etc.
•
As we shall see, this concept is important
in understanding the type of relationship…
Ch 18 4
Relationships Between Two
Variables
•
Nonmonotonic: two variables are
associated, but only in a very general
sense; don’t know “direction” of
relationship, but we do know that the
presence (or absence) of one variable
is associated with the presence (or
absence) of another.
•
At the presence of breakfast, we shall
have the presence of orders for coffee.
•
At the presence of lunch, we shall have
the absence of orders for coffee.
Ch 18 5
Nonmonotonic Relationship

Ch 18 6
Relationships Between Two
Variables
•
Monotonic: the general direction of a
relationship between two variables is
known
–
Increasing
–
Decreasing
•
Shoe store managers know that there is
an association between the age of a child
and shoe size. The older a child, the
larger the shoe size. The direction is
increasing, though we only know general
direction, not actual size.
Ch 18 7
Monotonic Increasing
Relationship
Ch 18 8
Relationships Between Two
Variables
•
Linear: “straight-line” association
between two variables
•
Here knowledge of one variable will
yield knowledge of another variable

•
“100 customers produce $500 in
revenue at Jack-in-the-Box” (p. 525)
Ch 18 9
Relationships Between Two
Variables
•
Curvilinear: some smooth curve
pattern describes the association
•
Example: Research shows that job
satisfaction is high when one first
starts to work for a company but goes
down after a few years and then back
up after workers have been with the
same company for many years. This
would be a U-shaped relationship.
Ch 18 10
Characterizing Relationships
Between Variables
1. Presence: whether any systematic
relationship exists between two
variables of interest
2. Direction: whether the relationship
is positive or negative
3. Strength of association: how strong
the relationship is: strong?
moderate? weak?
•
Assess relationships in the order

shown above.
Ch 18 11
Cross-Tabulations
•
Cross-tabulation: consists of rows and
columns defined by the categories
classifying each variable…used for
nonmonotonic relationships
•
Cross-tabulation table: four types of
numbers in each cell
–
Frequency
–
Raw percentage
–
Column percentage
–
Row percentage
Ch 18 12
Cross-Tabulations
•
Using SPSS, commands are
ANALYZE, DESCRIPTIVE
STATISTICS, CROSSTABS
•
You will find a detailed discussion of
cross-tabulation tables in your text,
pages 528-531.
Ch 18 13

Cross-Tabulations
Ch 18 14
Cross-Tabulations
•
When we have two nominal-scaled
variables and we want to know if
they are associated, we use cross-
tabulations to examine the
relationship and the Chi-Square test
to test for presence of a systematic
relationship.
•
In this situation: two variables, both
with nominal scales, we are testing
for a nonmonotonic relationship.
Ch 18 15
Chi-Square Analysis
•
Chi-square (X2) analysis: is the
examination of frequencies for two
nominal-scaled variables in a cross-
tabulation table to determine whether
the variables have a significant
relationship.
•
The null hypothesis is that the two
variables are not related.
•
Observed and expected frequencies:
Ch 18 16

Cross-Tabulations
•
Example: Let’s suppose we want to
know if there is a relationship
between studying and test
performance and both of these
variables are measured using
nominal scales…
Ch 18 17
Interpreting a Significant
Cross-Tabulation Finding
•
If the chi-square analysis determines
that you have a significant
relationship (no support for the null
hypothesis) you may use the
following to determine the nature of
the relationship:
–
The column percentages table or
–
The raw percentages table
Ch 18 18
Cross-Tabulations
•
Did you study for the midterm test? __yes
__no
•
How did you perform on the midterm test?
__pass __fail

•
Now, let’s look at the data in a crosstabulation
table:
Did You Study f or t he Test ? * How Did You Perf orm on t he
Test ? Crosst abulat ion
Count
77 2 79
3 18 21
80 20 100
Yes
No
Did You Study
for the Test?
Total
Pass Fail
How Did You Perform
on the Test?
Total
Ch 18 19
Cross-Tabulations
•
Do you “see” a relationship? Do you “see” the
“presence” of studying with the “presence” of
passing? Do you “see” the “absence” of
passing with the presence of not studying?
•
Congratulations! You have just “seen” a
nonmonotonic relationship.
Did You St udy f or t he Test ? * How Did You Perf orm on t he
Test ? Crosst abulat ion

Count
71 6 77
7 16 23
78 22 100
Yes
No
Did You Study
for the Test?
Total
Pass Fail
How Did You Perform
on the Test?
Total
Ch 18 20
Cross-Tabulations
•
Bar charts can be used to “see”
nonmonotonic relationships.
Did You Study f or the Test?
NoYes
Count
100
80
60
40
20
0
How Did You Perf orm
Fail
Pass

Ch 18 21
Cross-Tabulations
•
But while we can “see” this
association, how do we know there
is the presence of a systematic
association? In other words, is this
association statistically significant?
Would it likely appear again and
again if we sampled other students?
•
We use the Chi-Square test to tell us
if nonmonotonic relationships are
really present.
Ch 18 22
Cross-Tabulations
•
Using SPSS, commands are
ANALYZE, DESCRIPTIVE
STATISTICS, CROSSTABS and
within the CROSSTABS dialog box,
STATISTICS, CHI-SQUARE.
Ch 18 23
Chi-Square Analysis
•
Chi-square analysis: assesses
nonmonotonic associations in cross-
tabulation tables and is based upon
differences between observed and
expected frequencies

•
Observed frequencies: counts for
each cell found in the sample
•
Expected frequencies: calculated on
the null of “no association” between
the two variables under examination
Ch 18 24
Chi-Square Analysis
•
Computed Chi-Square values:
Ch 18 25
Chi-Square Analysis
•
The chi-square distribution’s shape
changes depending on the number of
degrees of freedom
•
The computed chi-square value is
compared to a table value to
determine
statistical
significance